Fibnacci Method

In mathematics, the Fibonacci numbers are the numbers in the following integer sequence:

fibnacci_7.png (1127 bytes)

The sequence  of Fibonacci numbers is defined by the recurrence relation

fibnacci_8.png (487 bytes)

where

fibnacci_9.png (678 bytes)

For large N, Fibonacci fraction fibnacci_10.png (533 bytes) converges to golden section ratio (0.618034…):

The following diagram is showing how Fibnacci number is used in optimization search.

golden_1.jpg (7984 bytes)

fibnacci_2.jpg (6294 bytes)

Fibonacci numbers fibnacci_4.jpg (1036 bytes) is determined by

fibnacci_5.jpg (3548 bytes)

fibnacci_6.jpg (2359 bytes)

fibnacci_1.jpg (31337 bytes)

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